• 대한수학회논문집
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• 제17권2호
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• pp.253-260
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• 2002

For an outer action $\alpha$ of a finite group G on a factor M, it was proved that H is a, normal subgroup of G if and only if there exists a finite group F and an outer action $\beta$ of F on the crossed product algebra M $\times$$_{\alpha}$ G = (M $\times$$_{\alpha}$ F. We generalize this to infinite group actions. For an outer action $\alpha$ of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When $\alpha$ satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action $\alpha$ of a compact group G and a closed normal subgroup H, we prove $M^{G}$ = ( $M^{H}$)$^{{beta}(G/H)}$for a minimal action $\beta$ of G/H on $M^{H}$.f G/H on $M^{H}$.TEX> H/.

• Journal of Oral Medicine and Pain
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• 제11권1호
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• pp.67-78
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• 1986

This study was attempted to identify the emotional characteristics of temporomandibular disorder patients. The author applied one of the self-report modes of psychological measurement, Symptom Chechlist-90-Revision. The subjects were 219 TM disorder patients who visited the Department of Oral Diagnosis and Oral Medicine, Seoul National University Hospital during the period from December 1985 to September 1986. All the patients were divided into subgroup according sex, age, duration of symptoms, presence or absence of T-scores of each symptom dimension and global index. The obtained result were as follows : 1. Mean value of T-scores of each symptom dimension and global of the overall patients was within normal range. The two higher mean values of T-scores among 9 symptom dimensions were those of SOM and ANX. 2. Mean values of T-scores of females were higher than those of males in the O-C, DEP, ANX, HOS, PSY dimensions and all global indices, and there was a significant difference in the distribution of T-scores of the SOM dimension between males and female(P<0.05). 3. There was no significant difference between the subgroup under 30 years and the subgroup 30 years or older. 4. The subgroup with symptoms for 6 months or longer showed the higher mean values of T-scorers in the SOM, O-C, I-S, DEP, ANX, PHOB, PAR, PSY dimensions and all global indices compared with the subgroup with symptoms for shorter than 6 months. 5. The subgroup with pain showed the higher mean values of T-scores in all the symptom dimensions except the PAR in comparison with the subgroup with other complaints than pain, and there was a significant difference in the distribution of T-scores of the PST index between the pain subgroup and the non-pain subgroup(P<0.05). There was a significant difference in the distribution of T-scores of the PHOB dimension between the high-school graduates subgroup and the college graduates subgroup(P<0.05).

• Korean Journal of Mathematics
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• 제6권2호
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• pp.319-322
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• 1998

For an M-group G, it is shown that a normal subgroup of G whose order is coprime to its index is an M-group.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.181-189
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• 2011

Let G be a group and X be a nonempty set and H be a subgroup of G. For a given ${\phi}_G\;:\;G{\times}X{\rightarrow}X$, a group action of G on X, we define ${\phi}_H\;:\;H{\times}X{\rightarrow}X$, a subgroup action of H on X, by ${\phi}_H(h,x)={\phi}_G(h,x)$ for all $(h,x){\in}H{\times}X$. In this paper, by considering a subgroup action of H on X, we have some results as follows: (1) If H,K are two normal subgroups of G such that $H{\subseteq}K{\subseteq}G$, then for any $x{\in}X$ ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_H}(x)$) = ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_K}(x)$) = ($orb_{{\phi}_K}(x)\;:\;orb_{{\phi}_H}(x)$); additionally, in case of $K{\cap}stab_{{\phi}_G}(x)$ = {1}, if ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}H}(x)$) and ($orb_{{\phi}_K}(x)\;:\;orb_{{\phi}_H}(x)$) are both finite, then ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_H}(x)$) is finite; (2) If H is a cyclic subgroup of G and $stab_{{\phi}_H}(x){\neq}$ {1} for some $x{\in}X$, then $orb_{{\phi}_H}(x)$ is finite.

• BMB Reports
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• 제32권1호
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• pp.25-27
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• 1999

Otitis media with effusion (OME) is an inflammatory disease of the middle ear cleft. Oxygen free radicals have been implicated in a variety of inflammatory disorders. Oxygen free radicals may also be involved in the pathogenesis of OME. To evaluate the involvement of oxygen free radicals in the pathogenesis of OME, the level of malondialdehyde, which gives an index of lipid peroxidation by oxygen free radicals, was measured by the reaction with thiobarbituric acid. Malondialdehyde level in the middle ear fluid from the OME group was higher than that in the normal control group. Malondialdehyde level in the middle ear fluid from a mucoid subgroup was higher than that in the serous subgroup. Malondialdehyde levels in the middle ear fluid from the serous subgroup was significantly correlated with symptom duration. The Pearson correlation coefficient between malondialdehyde levels in the middle ear fluid from the serous subgroup and symptom duration was 0.842 (P<0.05). These results indicate that lipid peroxidation by oxygen free radicals may be involved in the pathogenesis of human OME.

• 대한수학회지
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• 제50권6호
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• pp.1213-1222
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• 2013

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group G over a field $\mathbb{K}$ where the group G is a semidirect product of a normal abelian subgroup N and a subgroup H. The main results are proved with the assumption that char $\mathbb{K}$ does not divide |G| but there is no assumption made of $\mathbb{K}$ being algebraically closed.

• 대한수학회보
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• 제57권6호
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• pp.1475-1479
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• 2020

Let G be a finite group and ${\sigma}_1(G)={\frac{1}{{\mid}G{\mid}}}\;{\sum}_{H{\leq}G}\;{\mid}H{\mid}$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of G, we prove that if ${\sigma}_1(G)<{\frac{117}{20}}$, then G is solvable. This partially solves an open problem posed in [9].

• 대한수학회보
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• 제59권4호
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• pp.951-960
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• 2022

In this paper, we determine the finite p-group such that the intersection of its any two distinct minimal nonabelian subgroups is a maximal subgroup of the two minimal nonabelian subgroups, and the finite p-group in which any two distinct 𝓐₁-subgroups generate an 𝓐₂-subgroup. As a byproduct, we answer a problem proposed by Berkovich and Janko.

• 대한수학회보
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• 제38권2호
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• pp.317-324
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• 2001

A Cayley graph of a finite group G is called normal edge-transitive if its automorphism group has a subgroup which both normalized G and acts transitively on edges. In this paper, we consider Cayley graphs of finite cyclic groups, namely, finite circulant graphs. We characterize the normal edge-transitive circulant graphs and determine the normal edge-transitive circulant graphs of prime power order in terms of lexicographic products.

• 호남수학학술지
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• 제26권4호
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• pp.559-587
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• 2004

We study some properties of intuitionistic fuzzy normal subgroups of a group. In particular, we obtain two characterizations of intuitionistic fuzzy normal subgroups. Moreover, we introduce the concept of an intuitionistic fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.